LCM of 5 and 14
Understand the Problem
The question is asking for the least common multiple (LCM) of the numbers 5 and 14. To find the LCM, we typically look for the smallest number that is a multiple of both 5 and 14.
Answer
$70$
Answer for screen readers
The least common multiple (LCM) of 5 and 14 is $70$.
Steps to Solve
- Identify the multiples of each number
First, list some multiples of both 5 and 14.
Multiples of 5:
$5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100, 105, 110, 115, 120, 125, 130, 135, 140, 145, 150$
Multiples of 14:
$14, 28, 42, 56, 70, 84, 98, 112, 126, 140, 154, 168, 182, 196, 210$
- Find the common multiples
Look for the smallest number present in both lists of multiples. From our lists, the multiples of 5 are $5, 10, 15, 20, ...$ and the multiples of 14 are $14, 28, 42, ...$. The number that appears in both lists is:
- $70$
- Determine the least common multiple
Thus, the LCM of 5 and 14 is the smallest number that is present in both lists.
The least common multiple (LCM) of 5 and 14 is $70$.
More Information
The least common multiple is useful in various applications such as finding a common time when events happen simultaneously. The LCM helps in adding and subtracting fractions with different denominators, among other mathematical operations.
Tips
- Forgetting to list enough multiples: Ensure that you continue until you find a common multiple.
- Choosing a common multiple that is not the smallest: Always verify that you are selecting the least common one.
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